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Maximum moment

For standard load cases there are ready-made formulas for the maximum bending moment, so you avoid drawing the full diagram every time. A simply supported beam with a uniformly distributed load has its maximum moment at midspan, while a cantilever has it at the fixed end.

M_{max} = \dfrac{qL^2}{8}

simply supported, uniformly distributed load

M_{max} = \dfrac{PL}{4}

simply supported, point load at midspan

Symbols

$q$	uniformly distributed load	N/m
$P$	point load	N
$L$	span	m

Example

A 6 m beam with $q = 4$ kN/m:

$M_{max} = 4\cdot 6^2/8 = 18$ kNm.

Check whether the load is a point load or distributed – the formulas differ.

Practise bending of beams for free →

← Shear and moment · Deflection →

Part of Statics and Dynamics: Bending of beams.